Upvote:18
According to The Encyclopedia of the War of 1812: A Political, Social, and Military History:
In 1802 the British introduced the system of chevrons to distinguish NCO rank... Corporals wore two chevrons, and sergeants wore three... The color sergeant rank, introduced in 1813, had a single chevron with a regimental flag surmounted by a crown in the angle. Sergeant majors and quartermaster sergeants wore four chevrons. The rank of chosen man... had a single chevron... evolved into the rank of lance corporal...
The Royal Marines followed in 1810 - adopting Army ranks and insignia.
The Napoleonic French Army used chevrons on the upper arm to indicate veteran status - 1 chevron indicated 5-15 years of service, 2 chevrons for 15-20, and 3 chevrons for more than 20 years service. Ranks were indicated by stripes on the cuff.
The French introduced chevrons for ranks sometime before 1914, but only for some units - I'm having trouble finding exactly when.
The US Army introduced chevrons in 1847 - previously, a combination of button placement and cuff lacing indicated NCO rank.
As for the global prevalence of chevrons, the British established local regiments in many of their colonies, and introduced all manner of traditions and symbols, and these seem to have hung around even in countries where the British no longer rule. As countries gained independence from other various colonial powers, they have likely copied the chevrons and other insignia from the British and US armies.